College

What is the difference of the polynomials?

[tex]\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right)[/tex]

A. [tex]-x^3 + 6x^2 + 9[/tex]

B. [tex]-x^3 + 2x^2 - 9[/tex]

C. [tex]5x^3 - 2x^2 - 2x - 9[/tex]

D. [tex]5x^3 - 2x^2 + 2x + 9[/tex]

Answer :

To find the difference between the polynomials
$$ (5x^3 + 4x^2) - (6x^2 - 2x - 9), $$
we follow these steps:

1. **Distribute the Subtraction:**
The subtraction sign in front of the second polynomial affects every term inside the parentheses. Thus, we rewrite the expression as:
$$ 5x^3 + 4x^2 - 6x^2 + 2x + 9. $$

2. **Combine Like Terms:**
Identify and combine the like terms:
- The $x^3$ term: $$5x^3.$$
- The $x^2$ terms: $$4x^2 - 6x^2 = -2x^2.$$
- The $x$ term: $$2x.$$
- The constant term: $$9.$$

Combining these gives:
$$ 5x^3 - 2x^2 + 2x + 9. $$

3. **Final Answer:**
The difference of the given polynomials is:
$$ 5x^3 - 2x^2 + 2x + 9. $$

This is the simplified form of the expression.

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